AXIOM Meaning and
Definition
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An axiom is a fundamental statement or proposition that is commonly accepted and serves as a basic premise or starting point in a particular system of knowledge or reasoning. It is an irrefutable truth that is universally acknowledged and forms the foundation of a logical or mathematical theory.
Axioms are self-evident and do not require proof or justification. They are often presented as assumptions or conditions that are necessary for the establishment of logical or mathematical arguments. Axioms are considered to be universally valid and are not subject to debate or questioning.
In the realm of mathematics, axioms lay the groundwork for the development of mathematical theories and theorems. They define the fundamental concepts and relationships upon which mathematical reasoning is built. For example, in the field of geometry, Euclid's five postulates, such as “two points determine a line” and “the whole is greater than the part,” serve as axioms that establish the principles of geometric reasoning.
Axiomatic systems, which are built upon axioms, are critical for generating logical conclusions and deductions. By adhering to the underlying axioms, mathematicians can derive new theorems and proofs in a systematic and reliable manner.
Overall, axioms are indispensable in providing a solid and logical foundation for various systems of knowledge, allowing for the development and advancement of theories and ideas in fields such as mathematics, logic, and philosophy.
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A self-evident truth; an established principle in an art or science.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.
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Etymology of AXIOM
The word "axiom" has its roots in an ancient Greek term, "axios", which means "worthy" or "valuable". In Greek philosophy, an "axiom" referred to a self-evident or universally accepted truth or proposition. This concept was derived from the Greek verb "agein", meaning "to think" or "to lead". The term "axiom" was later borrowed into Latin as "axioma" and eventually entered the English language in the 15th century.
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